Make the sauce: Bring 1/4 cup water, the brown sugar and salt to a boil in a small saucepan, stirring until the sugar dissolves. Whisk in the cocoa powder until smooth. Remove from the heat and stir in the butter and vanilla. (You can refrigerate the sauce, covered, up to 3 days; reheat before serving.)
Make the sopaipillas: Heat 1/2 inch vegetable oil in a large deep skillet until a deep-fry thermometer registers 350 degrees F. Working in batches, fry the tortillas, turning once, until bubbly and golden on both sides, 1 to 2 minutes per batch. (Return the oil to 350 degrees F between batches.) Transfer to a paper towel-lined plate and sprinkle both sides generously with granulated sugar. Drizzle with the chocolate sauce.